Verified answer

(3 - √3)/(2 - √3)

Using conjugate of denominator,

(3 - √3)(2 + √3) / (2 - √3)(2 + √3)

= (6 + 3√3 - 2√3 - 3) / (4 - 3)

= (6 - 3 + √3)/1

= (3 + √3)

Ideally, you want to get rid of the root in the denominator, which you can do my multiplying the top and bottom by the conjugate.

For a+b, the conjugate is a-b.

So (3-√3)/(2-√3) = [(3-√3)(2+√3)]/[(2-√3)(2+√3)]

This gives (9+5√3)/(1)

So the answer is 9+5√3

It's already solved. If you meant to say rationalize the denominator, then

(2 √3)/(2 √3) (3 - √3)/(2 - √3) =

(6 - 2√3 3√3 - 3)/(4 - 3) =

(3 √3)/1 =

3 √3

Let under-root 3 be x, then

your question becomes

(3-x)/(2-x)

Now rationalise it. That is multiply the numerator and dinominator by (2+x)

Then it becomes (3-x)(2+x)/(2-x)(2+x)

You will get

(6+3x-2x-x^2)/(4-x^2)

here you will get

(6+x-x^2)/(4-x^2)

Now if you put the valu of x as root3

Then you will get

The answer as3+root 3

Note x^2 means x raised to power 2

And root 3 raised to power 2 is 3only.

6-3√3-2√3+3=

9-5√3

To get the exact answer to this kind of problem, multiply the numerator and denominator by

2+sqrt(3)

That will make the sqrt(3) terms drop out of the denominator, and you will just have the numerator to worry about:

(3-sqrt(3))/(2-sqrt(3) * (2+sqrt(3)/(2+sqrt(3)) = (3-sqrt(3))*(2+sqrt(3))/(4-3) =

(3-sqrt3)*(2+sqrt(3) = 6 - sqrt(3) -3 = 3 - sqrt(3)

In all such problems, if you have a-sqrt(b) in the denominator, multiply denominator and numerator by a+sqrt(b).

If you have a+sqrt(b) in the denominator, multiply by a-sqrt(b).

That way the messy terms will drop out of the denominator and you just have to deal with them in the numerator.

(3 - √3)/(2 - √3)

=> Rationalise the denominator, i.e.

(3 - √3) * (2 + √3)

---------------------

(2 - √3) * (2 + √3)

=> Use the difference of 2 squares in simplifying the denominator & also apply FOIL in removing the parentheses at the numerator, then you'll obtain

6 + 3√3 - 2√3 - 3

---------------------

(2)² - (√3)²

=> Collect like terms at the numerator, i.e.

(6 - 3 + 3√3 - 2√3)/(4 - 3)

= (3 - √3)/1

= 3 - √3 ...Ans.

3- sqrt 3 * 2+ sqrt 3

=================

2- sq rt 3 * 2+ sq rt 3 1

3 - sq rt 3

2+ sqrt 3

=========

3+sqrt 3-3

6-2 sqrt 3

============

3- sqrt 3

Hi there. Well it seems as if the people who have got the correct answer are the ones who have been given the poorest ratings. The answer is 4.732 or 3 + sqrt3.

(3 - √3)/(2-√3)

Rationalising the denominator we get

(3 - √3)(2+√3)/{(2-√3)(2+√3)}

={3 (2+√3)− √3(2+√3)}/{(2²-(√3)²}

={(6+3√3)− (2√3+3)}/{(4− 3)}

={6−3+3√3− 2√3)}/{(4− 3)}

={3+√3}/{1}

=3+√3